What is the integral of x/(e^{6x)} ?

The integral of x/(e^{6x)} is -1/6 e^{-6x}x-1/36 e^{-6x}+C

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integral of x/(e^{6x)}

\int \frac{x}{e ^{6 x}} d x

- \frac{1}{6} e^{- 6 x} x - \frac{1}{36} e^{- 6 x} + C

Solution steps

\int \frac{x}{e ^{6 x}} d x

Apply Integration By Parts

: - \frac{1}{6} e^{- 6 x} x - \int - \frac{1}{6} e^{- 6 x} d x

= - \frac{1}{6} e^{- 6 x} x - \int - \frac{1}{6} e^{- 6 x} d x

\int - \frac{1}{6} e^{- 6 x} d x = \frac{1}{36} e^{- 6 x}

= - \frac{1}{6} e^{- 6 x} x - \frac{1}{36} e^{- 6 x}

Add a constant to the solution

= - \frac{1}{6} e^{- 6 x} x - \frac{1}{36} e^{- 6 x} + C

3 x, \frac{3 x}{4}

\frac{d}{d x} ((2 x^{5} - 5 x^{3} + 7 x)^{4})

\int_{1}^{4} x^{2} + 2 x - 5 d x

\int (x - 5) d x

y = - 3 x + 12, y = 2 x^{2} - 11 x + 12

What is the integral of x/(e^{6x)} ?
The integral of x/(e^{6x)} is -1/6 e^{-6x}x-1/36 e^{-6x}+C